Systems and Matrices Test

Front

What is the formula to find the area of a triangle given its vertices?

Back

Area = 1/2 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|, where (x1, y1), (x2, y2), (x3, y3) are the vertices.

Front

How do you evaluate the determinant of a 2x2 matrix?

Back

For a matrix A = [[a, b], [c, d]], the determinant is ad - bc.

Front

What are the dimensions of a matrix?

Back

The dimensions of a matrix are given as rows x columns.

Front

What does it mean for two matrices to be multiplicative inverses?

Back

Two matrices A and B are multiplicative inverses if AB = I, where I is the identity matrix.

Front

How many columns are in a 2x12 matrix?

Back

A 2x12 matrix has 12 columns.

Front

What is the identity matrix?

Back

An identity matrix is a square matrix with ones on the diagonal and zeros elsewhere.

Front

How do you find the area of a triangle using coordinates?

Back

Use the formula: Area = 1/2 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|.

Front

What is a determinant?

Back

A determinant is a scalar value that is a function of the entries of a square matrix, providing important properties of the matrix.

Front

What is the significance of a zero determinant?

Back

A zero determinant indicates that the matrix is singular and does not have an inverse.

Front

How do you determine if two matrices are equal?

Back

Two matrices are equal if they have the same dimensions and corresponding elements are equal.